Nils Berglund | Waves escaping a ring of obstacles: Polar grid @NilsBerglund | Uploaded July 2024 | Updated October 2024, 4 minutes ago.
This is a simulation of waves originating from a point source crossing a set of circular obstacles placed on a "polar" grid, meaning that the locations form a regular grid in polar coordinates. Here there are 60 radial lines with 25 discs each. As one would expect, waves pass this lattice easier than for other arrangements seen on this channel. Still, diffraction has a large impact on the outgoing waves. The fact that the 60-fold symmetry is not preserved is probably due to round-off errors coming from the discretization.
This video has two parts, showing the same evolution with two different color gradients:
Averaged wave energy: 0:00
Wave height: 1:14
In the first part, the color hue depends on the energy of the wave, averaged over a sliding time window. In the second part, it depends on the height of the wave. The contrast has been enhanced by a shading procedure, similar to the one I have used on videos of reaction-diffusion equations. The process is to compute the normal vector to a surface in 3D that would be obtained by using the third dimension to represent the field, and then to make the luminosity depend on the angle between the normal vector and a fixed direction.
The color in the central region has been brightened to white, because the waves tend to make large-amplitude oscillations there, which would not be very pleasant to watch.
There are absorbing boundary conditions on the borders of the simulated rectangle. The display at the right shows a time-averaged version of the signal near the right boundary of the simulated rectangular area. More precisely, it shows the square root of an average of squares of the respective field value (wave height or energy).
Render time: 30 minutes 38 seconds
Compression: crf 23
Color scheme: Part 1 - Magma by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Part 2 - Twilight by Bastian Bechtold
github.com/bastibe/twilight
Music: "Desert Planet" by Quincas Moreira@QuincasMoreira
See also
https://images.math.cnrs.fr/des-ondes-dans-mon-billard-partie-i/ for more explanations (in French) on a few previous simulations of wave equations.
The simulation solves the wave equation by discretization. The algorithm is adapted from the paper hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf
C code: github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!
#wave #diffraction
This is a simulation of waves originating from a point source crossing a set of circular obstacles placed on a "polar" grid, meaning that the locations form a regular grid in polar coordinates. Here there are 60 radial lines with 25 discs each. As one would expect, waves pass this lattice easier than for other arrangements seen on this channel. Still, diffraction has a large impact on the outgoing waves. The fact that the 60-fold symmetry is not preserved is probably due to round-off errors coming from the discretization.
This video has two parts, showing the same evolution with two different color gradients:
Averaged wave energy: 0:00
Wave height: 1:14
In the first part, the color hue depends on the energy of the wave, averaged over a sliding time window. In the second part, it depends on the height of the wave. The contrast has been enhanced by a shading procedure, similar to the one I have used on videos of reaction-diffusion equations. The process is to compute the normal vector to a surface in 3D that would be obtained by using the third dimension to represent the field, and then to make the luminosity depend on the angle between the normal vector and a fixed direction.
The color in the central region has been brightened to white, because the waves tend to make large-amplitude oscillations there, which would not be very pleasant to watch.
There are absorbing boundary conditions on the borders of the simulated rectangle. The display at the right shows a time-averaged version of the signal near the right boundary of the simulated rectangular area. More precisely, it shows the square root of an average of squares of the respective field value (wave height or energy).
Render time: 30 minutes 38 seconds
Compression: crf 23
Color scheme: Part 1 - Magma by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Part 2 - Twilight by Bastian Bechtold
github.com/bastibe/twilight
Music: "Desert Planet" by Quincas Moreira@QuincasMoreira
See also
https://images.math.cnrs.fr/des-ondes-dans-mon-billard-partie-i/ for more explanations (in French) on a few previous simulations of wave equations.
The simulation solves the wave equation by discretization. The algorithm is adapted from the paper hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf
C code: github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!
#wave #diffraction
